Problem: The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives $18.6$ years; the standard deviation is $3.8$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a gorilla living between $14.8$ and $22.4$ years.
Explanation: $18.6$ $14.8$ $22.4$ $11$ $26.2$ $7.2$ $30$ $68\%$ We know the lifespans are normally distributed with an average lifespan of $18.6$ years. We know the standard deviation is $3.8$ years, so one standard deviation below the mean is $14.8$ years and one standard deviation above the mean is $22.4$ years. Two standard deviations below the mean is $11$ years and two standard deviations above the mean is $26.2$ years. Three standard deviations below the mean is $7.2$ years and three standard deviations above the mean is $30$ years. We are interested in the probability of a gorilla living between $14.8$ and $22.4$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $68\%$ of the gorillas will have lifespans within 1 standard deviation of the average lifespan. The probability of a particular gorilla living between $14.8$ and $22.4$ years is ${68\%}$.